Find w(4) for the function w(x) = 3x + 7.

If y is directly proportional to x^2, when x is halved, y becomes 0.25 times its original value. Given the original value of y is 10, when x is halved, the new y is 2.5.

When we say that y is directly proportional to x^2, it means there exists a constant of proportionality (let's call this 'k') such that the equation y = k*(x^2) always holds. From the problem, we know that y=10 for a certain x, let's square this x sometimes referred as x2 (we could say [tex]x2 = (x^1.5)^2).[/tex]

If x is halved, the new x which we can call [tex]x1 = 0.5*x2[/tex], then substitute x1 in the equation of direct proportion we get [tex]y1 = k*(0.5 *2)^2 = y*0.25[/tex], this is because (0.5)^2 is 0.25. So, the new y when x is halved (y1) will be 0.25 as much as the original y. Therefore, if your initial y was 10, your new y would be y1 = 10*0.25 which equals 2.5.

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The simultaneous equations 3x-3y=3 and y=-5x-17 can be solved using substitution, resulting in the solution x = -8/3 and y = -11/3.

To solve the simultaneous equations 3x-3y=3 and y=-5x-17, we can use substitution or elimination. Substitution is straightforward since we already have y expressed in terms of x in the second equation. We can substitute y=-5x-17 into the first equation:

Now, plug x back into y=-5x-17 to find y:

The solution to the system of equations is x = -8/3 and y = -11/3.

To find the number of eggs needed for 56 slices of pumpkin pie when the recipe calls for 1 egg for 8 slices, simply set up a proportion and solve. In this case, you would need 7 eggs for 56 slices of pie.

To determine how many eggs are needed to make 56 slices of pumpkin pie, we use a proportion. Given that 1 egg makes 8 slices of pie, we set up the proportion as follows:

Solving for x, which represents the number of eggs needed for 56 slices, we get that x = 7 eggs.

Answer:

all real numbers less than or equal to 3

Step-by-step explanation:

The range of the function is set of all y value for which the function is defined

To find out the range we look at the maximum or minimum point on the graph

Maximum point on the graph that is vertex is (-1,3)

x=-1 and y=3

The graph of y is below 3 (vertex)

So the range of the function is set of all real numbers less than or equal to 3

Answer:

[tex]\frac{1}{5} ;\frac{2}{10} ;\frac{3}{15}[/tex]

Step-by-step explanation:

To find the three ratios we only have to find the most simple ratio of [tex]\frac{7}{35}[/tex], and then find the other ratios that are equal to it.

So, [tex]\frac{7}{35} = \frac{1}{5}[/tex]

Also, [tex]\frac{1}{5} =\frac{2}{10}[/tex], by multiplying by two each part of the fraction.

Similarly, [tex]\frac{3}{15} = \frac{1}{5}[/tex], by multiplying by three.

Therefore, comparing all these ratios, all are the same, they are equal to [tex]\frac{1}{5}[/tex]. So, the option that correctly has these choices is D.

Answer:

Option a. 0

Step-by-step explanation:

As we know if we draw two circles with same center but with the different radii, they neither touch each other nor intersect. This is true not only for two circles but for infinite number of the circles having the same center. They never have the common points to share. Set of points lying on each concentric circles are different.

Therefore Option a. 0 points is the correct answer.

Answer:

The value of x is 16 .

Step-by-step explanation:

Definition of vertically opposite angles

Two lines crosses angles opposite to each other are called vertically opposite angle .

Thus

(2x + 13)° = (3x-3)°

(Vertically opposite angles )

2x + 13 = 3x-3

2x - 3x = -3-13

-x = -16

x = 16

Therefore the value of x is 16 .

Answer:

D

Step-by-step explanation:

The horizontal axis of the graph is Salary.

Given there is a positive correlation between salary and education, means that as if education increase, salary increase OR if education decrease, salary decrease, and vice versa.

Out of the 4 choices, they wanted to know the one that requires LEAST education. So we will look at the bar that has LEAST salary.

Looking at the graph and bars, out of the 4 choices, Surveyor has the LEAST SALARY, so SURVEYOR would require LEAST EDUCATION. Answer choice D is right.

The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}.[/tex] Option (d) is correct.

Further Explanation:

Given:

The options are as follows,

(a). Accountant

(b). Architect

(c). Pharmacist

(d). Surveyor

Explanation:

Correlation is a relationship between the two events. The change in one will affect the in change of another one.

There are two type correlations.

A positive correlation mean that if one increases the second event will also increase and if one decreases the second event will also decreases.

A negative correlation mean that if one increases the second event will also decrease and if one decreases the second event will also increase.

There is a positive correlation between salary and education.

The least salary in the given option is of surveyor and has least education.

The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}[/tex]. Option (d) is correct.

Learn more:

Answer details:

Grade: High School

Subject: Statistics

Chapter: Correlation

Keywords: correlation, salary, education, positive correlation, based, careers, least education, accountant, architect, pharmacist, surveyor, negative correlation, average salaries, personal trainer,  

7 × 30 = 7 × 3 tens.

To solve 7 × 30 in terms of tens, we first observe that 30 can be written as 3 tens since 30 equals 3 × 10.
Therefore:

7 × 30 can be rewritten as 7 × (3 × 10), which simplifies to 7 × 3 tens.

So, 7 × 30 = 7 × 3 tens.

Answer:

and only if they have the same slope. Any two vertical lines are parallel. Therefore, the slope of AB is -8 if AB is parallel to CD.

Step-by-step explanation:

The 38th power, [tex]i^{38[/tex] simplifies to -1.

To simplify [tex]\( i^{38 \),[/tex] you can start by recognizing the pattern that powers of i repeat every four terms. This means that [tex]\( i^{4\),[/tex]  equals 1, [tex]\( i^{8 \),[/tex]  also equals 1, and so on. Therefore,  [tex]\( i^{38 \),[/tex]can be simplified as follows:

[tex]\[ i^{38} = i^{4 \cdot 9 + 2} \][/tex]

Since [tex]\( i^4 \)[/tex] is equal to 1, we have:

[tex]\[ i^{38} = (i^4)^9 \cdot i^2 = 1^9 \cdot (-1) = -1 \][/tex]

So,[tex]\( i^{38} \)[/tex] simplifies to -1.

Complete question is:

Simplify i³⁸. [i=√(-1)]

The correct two-way table for comparing the car color choices of eight surveyed individuals by gender is Option D, which shows 2 females choosing green and 2 blue, while 1 male chose green and 3 chose blue.

The question is about analyzing a two-way table that compares categorical data: gender and car color preferences. To find the correct table, we need to tally the choices made by each person based on the information given and compare it to the options provided in the answer choices. By counting the number of times each gender chose each color, we can determine the accurate representation of the data.

For females, 2 chose green and 2 chose blue.

For males, 1 chose green and 3 chose blue.

Given this information, the correct two-way table that compares the categorical data is:

Option D.

            Green Blue

Female   2        2

Male        1         3

This table correctly captures the car color preferences by gender among the eight people surveyed.

Answer: A. AB=QR,BC=RS

Step-by-step explanation:

The congruence property of congruence triangle CPCTC says that the corresponding parts of congruent triangles are congruent.

From the given figure, we have

[tex]\angle{A}\cong\angle{Q}\\\angle{C}\cong\angle{S}[/tex]

[tex]\overline{AC}=\overline{QS}[/tex]

The other congruent parts in the triangle.

[tex]\overlien{AB}\cong\overlien{QR}[/tex] [∵ AB corresponds QR]

[tex]\\\\\overlien{BC}\cong\overlien{RS}[/tex]  [∵BC corresponds RS]

The original price of the shoes can be found by dividing the current price, $52, by 0.85, which yields an original price of approximately $61.18.

The current price of a pair of shoes is $52, which is 15% lower than it was last week. To find the original price, you can set up an equation where the original price minus 15% of the original price equals the current price of $52.

Let x represent the original price. The equation is then x - 0.15x = $52. Simplify this to 0.85x = $52. Divide both sides by 0.85 to solve for x.

x = $52 / 0.85

x = $61.18

Therefore, the price of the shoes last week was approximately $61.18.

The detailed answer provides the solutions to a series of questions involving finding specific values for y given x in various exponential equations, as well as recognizing the relationship between graphs of exponential functions and identifying which equations are not exponential.

1. If (-1, y) lies on the graph of y = 3ˣ+1, then y equals the value of the function when x is -1. Therefore, y = 3⁻¹ + 1 which simplifies to y = 1/3 + 1 = 4/3, which is not one of the provided options.

2. If (x, 1/100) lies on the graph of y = 10ˣ, then we need to find the value of x such that 10ˣ equals 1/100. 10ˣ = 1/100 is equivalent to 10ˣ = 10⁻², so x = -2.

3. If (-1, y) lies on the graph of y = 2²ˣ, we substitute x with -1. Then y = 2²*⁻¹ = 2⁻² = 1/4.

4. The relationship between the graphs of y = 2ˣ and y = 2⁻ˣ is that they are reflections over the y-axis. When x is replaced by -x in the function, the resulting graph is a reflection over the y-axis.

5. If (3, y) lies on the graph of y = -(2ˣ), then y is the negative value of 2 raised to the power of 3, which is -8. So, y = -8.

6. Among the given equations, y = -2ˣ is not exponential because it lacks the variable as an exponent. So, y = -2ˣ is not exponential.

7. If (-2, y) lies on the graph of y = 4ˣ, then y = 4⁻² = 1/16.

8. If (-3, y) lies on the graph of y = 3⁻ˣ, then y = 3⁻⁽⁻³⁾ = 3³ = 27.

9. If (-3, y) lies on the graph of y = 3ˣ, then y = 3⁻³ = 1/27.

10. If (-3, y) lies on the graph of y = (1/2)ˣ, then y = (1/2)⁻³ = 2³ = 8.

The correct equation for the line that passes through the point (2, 4) with a slope of 3 is 'y - 4 = 3(x - 2)' using the point-slope form of a linear equation.

The equation that represents the line passing through the point (2, 4) with a slope of 3 is y - 4 = 3(x - 2). To find the equation of a line given a point and a slope, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope of the line.

Since the line must pass through (2, 4) and the slope (m) is 3, we plug these values into the point-slope form to get the correct equation.

Answer: There can be made 40 smallest game boards.

Step-by-step explanation:

Since we have given that

Number of rows = 8

Number of spaces in each row = 10

we need to find the smallest game board that can be made.

As we know that For Smallest we always find "L.C.M" because L.C.M. stands for least common multiple.

So, L.C.M. of 8 and 10 = 40

Hence, there can be made 40 smallest game boards.